So here’s that post:

Eddie: Would the same physicists all say that “the standard model is a true, or approximately true, depiction of nature?”

I don’t know about physicists.

As I see it, the standard model is neither true nor false as a depiction of nature. Our concept of “true” does not allow us to make such a judgment of the standard model.

Here’s the problem:

There is nothing at all that can be said directly about nature. In order to say something, we need words and we need a standard way of attaching those words to nature. Until we have the words and the standards, there is no basis for saying anything.

The role of the standard model is to provide us with those words and standards which would allow us to say things about nature. So the standard model, or some suitable replacement, is a prerequisite to being able to have true or approximately true depictions of nature.

I look at the cosmology of Genesis 1 in about the same way. In its time, it provided a vocabulary and a set of standards on how to have true depictions of nature. So I tend to see that cosmology as neither true nor false, but as setting the stage to be able to make true depictions. But, of course, it has been superseded by newer and better cosmologies.

This post is not about how to solve a crossword puzzle. It’s about what we can learn about truth by looking at those puzzles.

Let’s suppose that you have been working on a crossword puzzle. And you think you have it solved. So how can you tell whether you have the correct solution? That is the question that I wish to examine. And since “correct” is closely related to “true”, it is a question about truth.

Sudoku puzzles

Before looking more closely at crossword puzzles, let’s take a quick peek at Sudoku puzzles. They make a good contrast with crossword puzzles.

We cannot just take a sentence and ask if it is true. We first have to inquire about everything referenced by that sentence. If people don’t agree on the references, they won’t agree on the truth of the sentence.

It’s a rather obvious point. Yet it is often overlooked.

Earlier this year, I proposed a modest theory of truth, in which I suggested that we judge the truth of a sentence based on whether it conforms with standards. What I mainly had in mind, and what my example illustrated, were the standards that we follow for settling questions of reference. Likewise, my posts about carving up the world are really all about how we go about finding ways to reference parts of the world.

Consciousness

In a way, the problems of consciousness are also closely connected with reference. The so called “hard problem” arose because people thinking about AI (artificial intelligence) did not see how a computer could possibly be conscious. Well, of course it cannot be conscious. For to be conscious is to be conscious of something, to be conscious of a world. Consciousness depends on reference. Or, as philosophers usually say that, it depends on intentionality.

This continues my series of posts on truth. Up to now, my discussion has mainly been technical. But truth matters to us because we want to be able to say true things. We use natural language statements about the world (where “world” is understood broadly) in order to say those true things.

Linguistics is not my area, but I cannot avoid it completely. Chomsky’s linguistics is based on the idea that language is a syntactic structure. Presumably the semantics are an add-on to that underlying syntactic structure, although Chomsky doesn’t say much about how semantics makes it into language.

I very much disagree with Chomsky’s view of language. As I see it, language is primarily semantic. I see the rules of syntax as mostly an ad hoc protocol used for disambiguation. So today’s post will be mainly about semantics or meanings. This has to do with how words can refer to things in the world, or how words can be about something. This is related to the philosophical problem of intentionality (or aboutness) of language statements. Here I will be presenting only a broad overview. I expect to get into more details in future posts.

Carving up the world

Similarly, if I were to say “the cat is on the mat”, you would see that as true provided that I had followed the standards of the linguistic community in the way that I used the words “cat”, “on” and “mat”.

According to my theory of truth, we need standards for the use of words such as “cat”, “on” and “mat”, and we judge the truth of a statement based on whether it conforms to those standards.

We make decisions. That’s a good part of what we do. For example, I have just decided to compose a post about decision making.

But how do we make decisions? How do we decide?

Generally speaking, we make some decisions on the basis of what is true. And we make other decisions on the basis of what works best for us. That latter kind of decision is usually said to be a pragmatic choice.

Examples

If I am solving a mathematical problem such as balancing my checkbook, then I am making decisions based on truth. If I am working on a logic problem, again that is going to be making decisions based on truth.

I walk into a restaurant, look at the menu, and decide what to order. That’s normally a pragmatic choice. It need not be. Perhaps I have created a rule for myself that if it is Sunday I should order the first item on the menu, if it is Monday I should order the second item, etc. If I am exactly following those rules, then I am making a decision based on truth. But that isn’t what we normally do when ordering a meal at a restaurant.

I have previously discussed some of the problems that I have with the so-called correspondence theory of truth. In this post, I shall suggest my own theory.

I am describing it as modest, because it does not attempt to settle all truth questions. The use of “true” in ordinary language is a mess, and my theory will not attempt to address all such use. Rather, it is intended only for technical uses, such as in mathematics and science.

In my last post, I made a distinction between ordinary mathematical statements such as and the axiom systems (such as the Peano axioms) that we use to prove those ordinary statements. There is widespread agreement on truth questions about those ordinary mathematical questions. But there is less agreement about whether axioms are true. Mathematics can be done, without settling questions on the truth of the axioms used.

Coming up with axiom systems is also part of mathematics. But when a new axiom system is offered, the main concern is on whether that axiom system is useful. Whether the axioms are true is often not asked, perhaps because there isn’t a good way to decide. Axiom systems are usually adopted on a pragmatic basis. That is, they are adopted for their usefulness.

Something similar happens in science. The ideal gas laws of physics are a good example. Those laws are true only for an imagined ideal gas. They are false for any real gas. But although technically false, they provide a pretty good approximation of the behavior of real gases. And that makes them very useful. So, with the gas laws, we see important scientific laws that are adopted on a pragmatic basis, even though they might be technically false.

While this post is about mathematical truth, it is really intended as part of a series of posts about truth. The mathematics here will be light. I am choosing to discuss mathematical truth because some of the distinctions are clearer in mathematics. But I do intend it to illustrate ideas about truth that are not confined to mathematics.

Mathematicians actually disagree about mathematical truth. But the disagreements are mostly peripheral to what they do as mathematicians. So they usually don’t get into intense arguments about these disagreements.

Philosophy

First a little philosophical background.

There is a school of mathematics known as Intuitionism. This differs from the more common classical mathematics, in that it has a more restrictive view of what is allowed in a mathematical proof. And, consequently, it has a more restrictive view of truth. In particular, Intuitionists do not accept Cantor’s set theory.

Pilate famously asked the title question (John 18:38). I expect people have been asking that question for as long as they have been asking questions. For a good discussion of theories of truth, check the entry in the Stanford Encyclopedia of Philosophy.

Truth is a central concept in philosophy. But I am not at all satisfied with the way that it is used. Hence this post.

Correspondence

If you ask about truth, you may be answered with the correspondence theory. But the idea of “correspondence” is usually left unexplained. I sometimes see statements similar to:

A sentence is true if it corresponds to the facts.

A sentence is true if it expresses what is the case.

A sentence is true if it expresses the state of affairs.

The trouble with all of these, is that they seem to be roundabout ways of saying “A sentence is true if it is true.” And that does not say anything at all.

Note that the “heretic” in the title refers to me, and comes from this blog’s title.

I have long considered myself a scientific realist. At least, on some definitions, a scientific realist is one who believes that science provides the best available descriptions of the natural world. And, in that sense, I surely am a scientific realist.

I’ve been noticing that some people have been suggesting that I am an instrumentalist or an anti-realist. So they must be using a different notion of “scientific realism.” There’s a post, today, at Scientia Salon which gets into such an account of scientific realism:

Here, I will discuss that post and where I have difficulty with the way that it looks at science. My own view of science, and how it works, should be apparent from that discussion. And I think it will be clear that my own view is non-standard (and, in that sense, heretical).

In this post, I shall discuss Snoke’s review. I suppose that makes it a review of a review.

I have previously discussed Nagel’s book on this blog — you can find those posts with a search on the main blog page. I clearly disagreed with a lot of what Nagel wrote in his book. By contrast, Snoke seems to like the book.

While I disagree with Snoke about the book, I do think Snoke’s review is well worth reading. Nagel’s book is not to everyone’s taste, and some might find it a hard read. Snoke, in his review, gives a synopsis of what he sees are some of the important parts of the book. So I’ll recommend that you read the Snoke review, particularly if you want to get an overview of what Nagel was arguing.